Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

A. Ben Tal, S. Boyd, and A. Nemirovski

Math. Programming, Series B, 107:63-89, February 2006

In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set. The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to sythesize linear controllers for discrete time dynamical systems.